The second mode of the Melodic Minor Scale is called the Dorian♭2 or Phrygian #6 depending on which way you want to see it.

It's not a commonly used mode really thought adding b9 on a Dorian style vamp can be pretty cool, but will clash if other band members (especially keys players) are playing a natural 9 (quite common in a Dorian vamp). They'll need to be listening and react to your move or pre-plan it.

The scale formula for the Dorian b2 is below, it describes the interval distances between each note of the scale. Note the 4 Tones in a row that help give this scale it's unique quality.

	S		T		T		T		T		S		T
1		2		3		4		5		6		7		8

T = Tone [whole step] • S = Semitone [half step]

Comparison With Major Scale

Scales are always compared to the Major Scale to find the intervals used.

	I	II	III	IV	V	VI	VII	I
C Major Scale	C	D	E	F	G	A	B	C
C Dorian b2	C	Db	Eb	F	G	A	Bb	C
Equation	1	b2	b3	4	5	6	b7	1

As the name suggests it's easiest to think of this as a Dorian Mode with a b2 (or a Phrygian with a raised 6 if you dig that approach).

Chords And Extensions

Because we're thinking modally here we're looking at the individual chords you might use this scale over not the Chords In The Key of the Melodic Minor Scale.

The only use I find for this would be over a 13b9(sus4) which let's just say it ain't that common and I've pretty much only played over it when experimenting with this mode to get a vibe on it. Not something that has ever popped up! The 13b9 does from time to time but that takes a Diminished HW.